To be useful, a laser gyro has to overcome the lock-in problem that occurs at low rotational rates. Lock-in is caused by unavoidable scattering of some light from one resonator mode into the other by imperfections of the optical elements comprising the cavity. If the frequencies of the modes are not too different, there is a tendency of the modes to phase lock. For a gyro to be of practical use, it has to overcome this lock-in problem. A two-frequency gyro system may avoid lock-in by biasing the gyro so that it operates with a large output frequency for zero input rotation rate. To avoid problems in bias accuracy, the bias can be dithered so that bias instabilities may be eliminated from the output signal by time averaging. This dither approach, however, causes the gyro to go through lock-in twice per dither cycle. This causes the gyro to partially lose its phase coherence; thus an error of a fractional count is made per dither cycle. These errors add randomly giving a cumulative output angular error which increases with time. A four-frequency differential laser gyro system solves this problem by essentially operating two independent gyros in a single stable resonator sharing a common optical path, but statically biased in opposite senses by the same passive bias elements. In the differential output of these two gyros, the bias cancels while any rotation generated signals add, thereby giving a sensitivity twice that of the single two-frequency gyro and avoiding problems due to drifts in the bias. The four different frequencies are normally generated by using two different optical effects. First, a crystal polarization rotator is used to provide a direction-independent polarization causing the resonant waves to be nearly right-hand circularly polarized (RCP) and left-hand circularly polarized (LCP). The polarization rotation results from the refractive index of the rotator medium being slightly different for RCP and LCP waves. Second, a Faraday rotator is used to provide non-reciprocal polarization rotation, by having a slightly different refractive index for clockwise travelling waves than for counter-clockwise travelling waves. This causes the cw and ccw RCP waves to oscillate at slightly different frequencies while the cw and ccw LCP waves are similarly but oppositely split. This Faraday rotator may be a separate optical element consisting of a piece of optically isotropic material subjected to a longitudinal magnetic field, or it may be realized by applying such a magnetic field to the crystal rotator. Thus, there is a laser gyro operating with right circular polarization biased in one direction of rotation and another with left circular polarization biased in the opposite direction, the bias being cancelled by subtracting the two outputs. The operation of a basic four-frequency laser gyroscope is described in K. Andringa U.S. Pat. No. 3,741,657 issued June 26, 1972 and assigned to the present assignee.